perth and thing to do with kids

Hi everyone
Im an expat mum (born and raised in perth australia) living in europe with my husband and 2 child (1 and 4). im planing a visit over to perth to visit friends and family for about 6 weeks over christmas. its only myself and kids going as my husband cant get so much time of work, any way I have a few questions.

1) I would love some ideas of things i can do in perth with the kids, anything that is a must do. any really nice parks its been a while since i was last there so im am sure thing have changed

2) As a 4year old my oldest is still free when we travel on public transport but he is extremely tall for his age. he is alway mistaken for a child 2 or 3 years old than he is. my mum seems to think we are going to have problems trying to pass him of on public transport as a 4 year old. Has any one had a problem like this in perth or any where else in australia.

3) Im think of taking my 4 year old to adventure world ( leaving the baby with my mum at her house) and having a special day just the 2 of us. we would go during the week before christmas holidays start. Worth it or not? any other tips you could give me about adventure world. any other places we could go just the 2 of us.